In addition to the cost of estimating hyperparameters of the exact GP involving \(\mathcal {O}(n^3)\)  floating point operations, the prediction with the GP costs \(\mathcal {O}(n)\)  and \(\mathcal {O}(n^2)\)  operations, respectively, for the posterior mean and variance computation. Sparse GP models [1]} circumvent this overhead by identifying a subset \(m<n\)  of the training points, resulting in reduced computational costs that scale as \(\mathcal {O}(m^2n)\) , \(\mathcal {O}(m)\) , and \(\mathcal {O}(m^2)\)  for fitting, predicting mean, and predicting variance, respectively.
